One thing that irks me is redundant controls. For example, there was a game I used to play that had a "disable IP check" option, but if you enabled it without Game Operator permission then you would be permanently banned. I have no idea why they couldn't just give the GO that option instead of giving people a "ban me now" button...

Anyway, back to SO. Since a user cannot vote on their own questions or answers, what is the point of the arrows being there? It seems wasteful to have buttons that I cannot use (and it's annoying when I accidentally click them when trying to expand my vote score, but that's probably just me), and I think they should be removed.

What, so we're talking beauty over practicality now, on this, of all sites? Bloody hypocritical, that. Kieth has the best point which tallies with your last (secondary?) concern, in that they do have a use.
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Grant ThomasApr 2 '13 at 15:59

Although it may fool users into thinking they can vote for themselves once, it gives users feedback after voting so that they won't do it again.

Removing the arrows is likely to confuse people. It will likely lead some new users to think something is "wrong", without any explanation for why. They'll probably waste a few minutes refreshing the page or restarting the browser, and then end up posting a question here on meta.

I think displaying the arrows is the most effective way to inform people that they cannot vote for themselves without causing confusion.